Final answer:
To find the image and pre-image using the given translation, substitute the coordinates into the translation formula. For example, the image of A (-6, 3) is (-1, -6) and the pre-image of D' (12, 7) is (7, 16).
Step-by-step explanation:
a. To find the image of A (-6, 3), we substitute the coordinates into the translation formula. (x, y) = (x + 5, y - 9). So, the image of A is (-6 + 5, 3 - 9) = (-1, -6).
b. To find the image of (4, 8), we substitute the coordinates into the translation formula. (x, y) = (x + 5, y - 9). So, the image of (4, 8) is (4 + 5, 8 - 9) = (9, -1).
c. To find the image of (5, -3), we substitute the coordinates into the translation formula. (x, y) = (x + 5, y - 9). So, the image of (5, -3) is (5 + 5, -3 - 9) = (10, -12).
d. The image of A from question 1, which would be called A'', can be found by applying the translation (x, y) = (x + 5, y - 9) to the image of A. So, the image of A'' is (-1 + 5, -6 - 9) = (4, -15).
e. To find the pre-image of D' (12, 7), we need to apply the inverse translation (x, y) = (x - 5, y + 9) to the coordinates of D'. So, the pre-image of D' is (12 - 5, 7 + 9) = (7, 16).